On nonlinear nonlocal systems of reaction diffusion equations
type: Item
instance of: scholarly article
title: On nonlinear nonlocal systems of reaction diffusion equations
zbMATH Open document ID: 1474.35627
DOI: 10.1155/2014/804784
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The reaction diffusion system with anomalous diffusion and a balance law \(u_t + \left(- \Delta\right)^{\alpha / 2} u = - f \left(u, v\right)\), \(v_t + \left(- \Delta\right)^{\beta / 2} v = f \left(u, v\right)\), \(0 < \alpha\), \(\beta < 2\), is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction term \(f\) when \(0 < \alpha \leq \beta \leq 2\); (ii) no growth condition is imposed on the reaction term \(f\) when \(0 < \beta \leq \alpha \leq 2\).
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 7023109
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/804784
OpenAlex ID: W2132231021
Wikidata QID: Q59041646
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description: scientific article; zbMATH DE number 7023109